Merodio, J. and Ogden, R.W. (2006) On the equivalence of strong ellipticity in the material and spatial settings of finite elasticity. Zeitschrift für Angewandte Mathematik und Physik, 57(6), pp. 1096-1101. (doi: 10.1007/s00033-006-0078-1)
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Publisher's URL: http://dx.doi.org/10.1007/s00033-006-0078-1
Abstract
It is known from Shield's theorem that the equilibrium equations for the inverse deformation in finite elasticity are equivalent to those for the primary deformation. We review this result for compressible elastic solids and then use it to provide a simple proof that strong ellipticity in the material setting is equivalent to that in the spatial setting. The result is then extended to incompressible materials.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Ogden, Professor Raymond |
| Authors: | Merodio, J., and Ogden, R.W. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Zeitschrift für Angewandte Mathematik und Physik |
| ISSN: | 0044-2275 |
| ISSN (Online): | 1420-9039 |
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